{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8ca26045",
   "metadata": {},
   "source": [
    "# Chapter 3.Interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fffa7154",
   "metadata": {},
   "source": [
    "## 3.1 Lagrange interpolation\n",
    "\n",
    "## \n",
    "#### 拉格朗日插值的基本公式为：\n",
    "$$\n",
    "P_{n-1}(x) = a_1L_1(x)+a_2L_2(x)+……+a_nL_n(x)\n",
    "$$\n",
    "#### 其中: \n",
    "$$\n",
    "a_i = y_i\n",
    "$$\n",
    "$$\n",
    "L_i(x)=\\frac{x-x_1}{x_i-x_1}\\frac{x-x_2}{x_i-x_2}\\frac{…}{…}\\frac{x-x_{i-1}}{x_i-x_{i-1}}\\frac{x-x_{i+1}}{x_i-x_{i+1}}\\frac{…}{…}\\frac{x-x_n}{x_i-x_n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09eec949",
   "metadata": {},
   "source": [
    "#### 用Python进行拉格朗日插值的核心在于用两个循环分别计算$P_{n-1}(x)$和$L_i(x)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8261395f",
   "metadata": {},
   "source": [
    "## Step.1 写出拉格朗日插值的Python函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9e096287",
   "metadata": {},
   "outputs": [],
   "source": [
    "# python fucntion for Lagrange interpolation\n",
    "def interplag(x,xiList,yiList):\n",
    "    xiList = np.array(xiList)\n",
    "    yiList = np.array(yiList)\n",
    "    y = 0\n",
    "    for i in range(xiList.size):\n",
    "        ai = yiList[i]\n",
    "        li = 1\n",
    "        for j in range(xiList.size):\n",
    "            if i != j:\n",
    "                li = li * (x - xiList[j]) / (xiList[i] - xiList[j])\n",
    "        y = y + ai * li\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "157bbaea",
   "metadata": {},
   "source": [
    "## Step.2 给出差值的数据信息"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "754e9115",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dd132a84",
   "metadata": {},
   "outputs": [],
   "source": [
    "xiList = [0,1,1.5,3,5]\n",
    "yiList = [-1,2,3,1,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f25cf13d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize  =(8,6))\n",
    "plt.scatter(xiList,yiList,c = 'yellow',edgecolors = 'orange',s = 100)\n",
    "plt.xlabel(\"x\",fontsize = 10)\n",
    "plt.ylabel(\"y\",fontsize = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "717321b9",
   "metadata": {},
   "source": [
    "## Step.3 插值计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "087931ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "xList = np.arange(0,5.1,0.1)\n",
    "yList = [interplag(x,xiList,yiList) for x in xList]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0cb90ba1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c4372e1580>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize  =(8,6))\n",
    "plt.scatter(xiList,yiList,c = 'yellow',edgecolors = 'orange',s = 100)\n",
    "plt.xlabel(\"x\",fontsize = 10)\n",
    "plt.ylabel(\"y\",fontsize = 10)\n",
    "plt.plot(xList,yList,'c-')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876717ac",
   "metadata": {},
   "source": [
    "## Step.4 插值任意函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c01285bf",
   "metadata": {},
   "source": [
    "#### 插值cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ea2020bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "xiList = np.arange(0,np.pi,0.1)\n",
    "yiList = np.cos(xiList)\n",
    "\n",
    "xList = np.arange(0,np.pi,0.01)\n",
    "yList = [interplag(x, xiList, yiList) for x in xList]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b8b3da7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c4373ff220>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (8,6))\n",
    "plt.scatter(xiList,yiList,c = 'yellow',edgecolors = 'orange',s = 100)\n",
    "plt.xlabel(\"x\",fontsize = 10)\n",
    "plt.ylabel(\"y\",fontsize = 10)\n",
    "plt.plot(xList,yList,'c-')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
